2017/04/14 by Elif Uyanık, Uyanık, Elif, Murat H. Yurdakul +1
Mathematics · #46A45 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46A45
paper · pdf · doi:10.48550/arxiv.1704.04397
6 pages
arxiv created 2017/04/14 · arxiv updated 2017/04/17
Let l be a Banach sequence space with a monotone norm in which the canonical system (en) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between l-Köthe spaces, then there exists a continuous unbounded quasi-diagonal operator between them. Using this result, we study in terms of corresponding Köthe matrices when every continuous linear operator between l-Köthe spaces is bounded. As an application, we observe that the existence of an unbounded operator between l-Köthe spaces, under a splitting condition, causes the existence of a common basic subspace.